|
| |
|
|
A066951
|
|
Number of nonisomorphic connected graphs that can be drawn in the plane using n unit-length edges.
|
|
3
|
| |
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
K_4 can't be so drawn even though it is planar. These graphs are a subset of those counted in A046091.
|
|
|
REFERENCES
|
M. Gardner, The Unexpected Hanging and Other Mathematical Diversions. Simon and Schuster, NY, 1969, p. 80.
R. C. Read, From Forests to Matches, Journal of Recreational Mathematics, Vol. 1:3 (Jul 1968), 60-172.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
Up to five edges, every planar graph can be drawn with edges of length 1, so up to this point the sequence agrees with A046091 (connected planar graphs with n edges) [except for the fact that that sequence begins with no edges]. For six edges, the only graphs that cannot be drawn with edges of length 1 are K_4 and K_{3,2}. According to A046091, there are 30 connected planar graphs with 6 edges, so the sixth term is 28.
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,more,nice
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
Corrected, extended and reference added. a(7)=74 and a(8)=207 from Read's paper. - William Rex Marshall, Nov 16 2010
a(9) corrected (from version 2 [May 22 2013] of Salvia's paper) by Gaetano Ricci, May 24 2013
|
|
|
STATUS
|
approved
|
| |
|
|
